Predicting
the Structure
of the Solar CoronaDuring the July 22,
2009
Total Solar Eclipse

On Wednesday, July 22, 2009, a solar eclipse will be visible in the
equatorial regions spanning both hemispheres. A total eclipse
will occur within a narrow
corridor in eastern Asia and the Pacific Ocean. It will be
visible first on the northwestern coast of India at sunrise (just
before 01:00 UT) and continue through Nepal, Bangladesh, and Bhutan,
crossing into China, where it will be visible in several large cities,
including Shanghai. The moon's shadow will then cross into the
East China Sea, across Japan’s Ryukyu Islands, and on to Iwo Jima at
02:27 UT, the Marshall Islands, and the Gilbert Islands, ending in the
southern Pacific Ocean at 04:18 UT. Maximum eclipse will occur in
the Pacific Ocean at 02:35 UT, lasting 6 minutes
and 39 seconds. To
see a detailed description of the eclipse path, please
visit NASA's
Eclipse page. For useful information about eclipse
photography, please visit Fred
Espenak's Eclipse web site.

On July 9, 2009, we started an
MHD computation of the solar corona,
in
preparation for our prediction
of what the solar corona would look like during this eclipse. We
used
photospheric magnetic field data for Carrington rotation 2084, measured
up to June 26, 2009 by the MDI
magnetograph aboard the SOHO
spacecraft. We
typically also use magnetic field measurements from the Wilcox Solar Observatory
at Stanford and the National Solar Observatory SOLIS vector magnetograph at Kitt
Peak. A very useful prediction
of the photospheric solar magnetic field is carried out by Karel
Schrijver and Marc DeRosa at Lockheed
Martin.

A preliminary prediction of the state of the solar corona
during the
eclipse based on this data was posted on this web site on July 13,
2009.
This
preliminary prediction can be found here.
On July 15, 2009 we started a new calculation with
updated magnetic field data that was measured with MDI up to July 11,
2009.
This page now has the updated (and final) prediction, and was posted on
July 19, 2009.

Our prediction is based on a magnetohydrodynamic model of the solar
corona with improved energy transport. We used this model for the
first time to predict the structure of the corona prior to the March 29, 2006 total solar
eclipse. The improved energy equation model includes the
effects of coronal heating, the conduction of heat parallel to the
magnetic field lines, radiative losses, and the effect of Alfvén
waves. This produces a significantly better estimate of the
plasma temperature and density in the corona. For technical
details about our improved model, please see the publications
below. The prediction shown here uses our new
model, and allows
us to predict emission
in extreme ultraviolet (EUV) wavelengths and
X-rays, which can be compared with solar observations from the EIT imager on SOHO and the X-ray
instrument on Hinode,
in
addition to emission in
polarized white
light (polarization
brightness, pB) that is typically measured during an eclipse.

Some technical details about the calculation that was used to make our
final prediction can be found here.

For your curiosity, you can see the milestones in achieving our
prediction here.

The figure on the left shows the predicted polarization
brightness
(pB) in the solar corona for the eclipse expected on July 22, 2009 at
02:35 UT (corresponding to the moment of greatest eclipse in the
Pacific Ocean).
The state of
the
solar corona was computed using a 3D magnetohydrodynamic (MHD) simulation. The pB signal is
produced by white light scattered off electrons in the
coronal plasma. The image has been radially detrended using the Newkirk
vignetting function to account
for the fall-off of coronal brightness with distance from the
Sun.
Vertical (top) is terrestrial (geocentric) north. This is the
view of
the
Sun that would be seen by an observer on Earth with a camera aligned so
that vertical is toward the Earth's north pole. To view this
image
in a coordinate system aligned with solar north, click
here. Click the image to see it in greater detail.

Predicted polarization brightness (top left) together with
traces of
the magnetic field lines in the solar corona (top right) for the
eclipse
expected on July 22, 2009 at 02:35 UT (with terrestrial north
up).
The Sun's surface shows color contours of the radial component of the
measured
photospheric magnetic field from the MDI
magnetograph, showing the location of active regions
(strong magnetic fields). Click the images for higher resolution
pictures. To view these images in a coordinate system aligned
with
solar north, click here.

The photospheric magnetic field maps we use for our
calculations are built up from daily observations of the Sun during a
solar rotation. These maps give a good approximation of the Sun's
magnetic flux if the large-scale flux does not change much throughout a
rotation. Previously, we have computed coronal models for an
eclipse during the
declining
phase of the last solar cycle (November 3, 1994), for
three eclipses during solar minimum (October 24, 1995, March 29, 2006, and March 9, 1997), one
eclipse during the the early rising phase of solar
cycle 23 (February 26,
1998), one eclipse approaching solar maximum (August
11, 1999), and two eclipses near solar maximum (June 21, 2001 and December 4, 2002).

These figures show the evolution of the radial component (Br)
of the solar photospheric
magnetic field for three Carrington
rotations preceding the eclipse, as measured by the MDI
magnetograph aboard the SOHO spacecraft. We use smoothed
versions of these magnetic field maps in our calculations.

We
used the data for Carrington rotation
(CR) 2084 in our calculation for our preliminary eclipse prediction,
which was posted on July 13, 2009, and can be found here.
The last panel shows the magnetic
field data that was used for the
final eclipse prediction, which is posted on this page. That
calculation was started on July 15, 2009, and was posted on July 19,
2009.

These maps show the radial component of the magnetic field
deduced from
the measured photospheric
field as a function of latitude (vertical axis) and Carrington
longitude (horizontal axis). Red shows outward directed magnetic
field, and blue shows inward directed field. The dark regions
near the top and bottom indicate areas near the solar poles where it is
not possible to estimate the radial component of the magnetic field due
to projection effects. Click the images for
higher resolution pictures.

CR2083 (May 3 – 30, 2009)

CR2084 (May 30 – June 26, 2009)

CR2084+CR2085 (June 14 – July 11, 2009)

Images
and Movies of Coronal Emission in EUV and X-Rays

Our 3D MHD model with improved energy transport allows us to simulate
the emission from the corona in extreme ultraviolet and X-ray
wavelengths. The Sun can be observed in these wavelengths from
space. In particular, the SOHO/EIT, TRACE, and STEREO/EUVI, and Hinode/EIS
telescopes routinely take EUV images of the solar corona, and the Yohkoh/SXT (no longer
operating) and Hinode/XRT
telescopes image the soft X-ray Sun. Our simulated coronal
emission is available here.

Movies of
Polarization Brightness

We have made movies of the polarization brightness (pB) from our MHD
simulation. This illustrates visually how the solar corona
changes as a result
of solar rotation.

You
can also see a movie of pB with a blue background and a black disk
occulting the Sun: a QuickTime
version
(364 kbytes, recommended),
or a GIF
version
(4.4 Mbytes).

If your movie player can continuously loop a movie
while
playing it, set this option to "on" for the best effect.

Movie of Magnetic Field Lines

We have made a movie of the magnetic field lines and simulated emission
from the Hinode XRT telescope (Al mesh filter). This is a
simulated
"synoptic" XRT image wrapped on the sphere, so emission on the
limbs is not visible. Blue field lines are closed, green
field lines are open. This movie illustrates the relationship
of closed and open structures to features in emission.

Other web resources for the eclipse

Acknowledgements

Our work is supported by NASA, AFOSR and NSF through the Strategic
Capabilities program, by NASA's Heliophysics Theory Program
(HTP), by the Center
for Integrated
Space Weather Modeling (an NSF Science & Technology
Center), by NASA's
Supporting Research & Technology (SR&T) Program, and by NASA's
Living
With a Star (LWS) Program. We thank the staff at the Texas Advanced Computing Center
(TACC) for graciously providing us with dedicated time on their
massively parallel supercomputer Ranger,
and NASA's
Advanced Supercomputing Division
(NAS) for an allocation
on the Pleiades
supercomputer. Our calculations for the eclipse prediction were
performed on these computers. We thank Todd
Hoeksema of the Solar Physics Group
at Stanford University for providing us with timely access to
MDI magnetograph data and for
sharing the latest calibrated data
with us.